Preliminary SAT or National Merit Scholarship Qualifying Test Interview Questions

 
1.
Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?
2.
Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28.
3.
When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
4.
A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
5.
Given A = 265 and B = (264+263+262+...+20)
6.
The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.
7.
A piece of equipment cost a certain factory Rs. 600,000. If it depreciates in value, 15% the first year, 13.5% the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?
8.
Solve the inequality 33x-2 > 1
9.
The largest number amongst the following that will perfectly divide 101100 - 1 is
10.
What is the highest power of 7 in 5000!? (5000! means factorial 5000)
11.
What is the total number of different divisors including 1 and the number that can divide the number 6400?
12.
How many four digit numbers exist which can be formed by using the digits 2, 3, 5 and 7 once only such that they are divisible by 25?
13.
A certain number when successfully divided by 8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder when the number is divided by the product of 8 and 11, viz 88?
14.
What is the reminder when 91 + 92 + 93 + ...... + 99 is divided by 6?
15.
How many times will the digit 0 appear between 1 and 10,000?
16.
What is the total number of different divisors of the number 7200?
17.
What is the least number that should be multiplied to 100! to make it perfectly divisible by 350?